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A theory invoking concepts from differential geometry of generalized Finsler space in conjunction with diffuse interface modeling is described and implemented in finite element (FE) simulations of dual-phase polycrystalline ceramic microstructures. Order parameters accounting for fracture and other structural transformations, notably partial dislocation slip, twinning, or phase changes, are dimensionless entries of an internal state vector of generalized pseudo-Finsler space. Ceramics investigated in computations are a boron carbide-titanium diboride (B4C-TiB2) composite and a diamond-silicon carbide (C-SiC) composite. Deformation mechanisms-in addition to elasticity and cleavage fracture in grains of any phase-include restricted dislocation glide (TiB2 phase), deformation twinning (B4C and β-SiC phases), and stress-induced amorphization (B4C phase). The metric tensor of generalized Finsler space is scaled conformally according to dilatation induced by cavitation or other fracture modes and densification induced by phase changes. Simulations of pure shear consider various morphologies and lattice orientations. Effects of microstructure on overall strength of each composite are reported. In B4C-TiB2, minor improvements in shear strength and ductility are observed with an increase in the second phase from 10 to 18% by volume, suggesting that residual stresses or larger-scale crack inhibition may be responsible for toughness gains reported experimentally. In diamond-SiC, a composite consisting of diamond crystals encapsulated in a nano-crystalline SiC matrix shows improved strength and ductility relative to a two-phase composite with isolated bulk SiC grains.

Computational Modeling of Dual-Phase Ceramics with Finsler-Geometric Phase Field Mechanics